Those AT831's were my 1st set of mics & they made pretty good recordings the few times I used them. I didn't like stealthing very much. I'd suggest them especially for the price. Great bang for the buck & right in your price range. You can also buy different caps for them.
You need the battery box with the bass rollover option. I've never seen/used that small box but it looks good. I'd take advantage of the 24 inch cord as well. They didn't offer that when I bought mine.
Search this board & the archives. You'll find a plethora of info on these & other stealth mics.
Welcome to the boards, T+ & good luck picking something out. What are you recording on?